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Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures

Abstract

This paper is a coalgebra version of Positselski (Rendiconti Seminario Matematico Univ. Padova 143: 153–225, 2020) and a sequel to Positselski (Algebras and Represent Theory 21(4):737–767, 2018). We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras \({\mathcal {C}}\) and \({\mathcal {D}}\). For any such complex \({\mathcal {L}}^{\scriptstyle \bullet }\), we construct a triangulated category endowed with a pair of (possibly degenerate) t-structures of the derived type, whose hearts are the abelian categories of left \({\mathcal {C}}\)-comodules and left \({\mathcal {D}}\)-contramodules. A weak version of pseudo-derived categories arising out of (co)resolving subcategories in abelian/exact categories with enough homotopy adjusted complexes is also considered. Quasi-finiteness conditions for coalgebras, comodules, and contramodules are discussed as a preliminary material.

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Acknowledgements

I am grateful to Jan Št’ovíček for helpful discussions. The author’s research is supported by the GAČR project 20-13778S and research plan RVO: 67985840.

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Correspondence to Leonid Positselski.

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Communicated by Vladimir Hinich.

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Positselski, L. Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures. Appl Categor Struct (2021). https://doi.org/10.1007/s10485-021-09660-y

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Keywords

  • Comodules and contramodules
  • Derived, coderived, and contraderived categories
  • Pseudo-derived categories and pseudo-derived equivalences
  • Dualizing, dedualizing, and pseudo-dualizing complexes
  • t-structures of the derived type